Position control servo mechanism using a trigonometric function generator



Dec. 31, 1968 F. w. HARTLEY 3,419,774

POSITION CONTROL SERVO MECHANISM USING A TRIGONOMETRIC FUNCTIONGENERATOR Filed Feb. 2. 1965 PRIOR ART FIG. 1.

Cos(A-6).Tun B United States Patent 3,419,774 POSITION CONTROL SERVOMECHANISM USING A TRIGONOMETRIC FUNCTION GENERATOR Frederick WalterHartley, Hayes, England, asslgnor to Electric & Musical IndustriesLimited, Hayes, England, a company of Great Britain Filed Feb. 2, 1965,Ser. No. 429,858 Claims priority, application Great Britain, Feb. 7,1964, 5,247/ 64 4 Claims. (Cl. 318-18) A position control servomechanism using a resolver with quadrature windings on both rotor andstator, with command signals in the form of alternating voltagesproportional to the sine and cosine of an angle respectively applied tothe windings of the stator. Output voltages are derived from thewindings of the rotor and one of these voltages is applied to anauto-transformer from which is derived a fraction, such as the tangentfunction, dependent on a second angle, and the other output voltage andthe fraction from the auto-transformer are summed to produce an errorsignal which is used to drive a servo motor rotating the rotor of theresolver. This servo mechanism tends to set the resolver to a positionrepresenting the sum of the two angles. If the second angle is alwayssmall the fraction derived from the auto-transformer can be linearlyrelated to the second angle.

This invention relates to a position control servo mech anism of thetype using a trigonometric function generator, from which signals areapplied to a resolver coupled to a part to be positioned.

It is a requirement in position control apparatus that a device be setto a given position in response to a command. The command may, forexample, be provided by the manual setting of a series of control knobsor by uniselector, relay or transistor switches which are arranged toprovide alternating voltages the amplitudes of which are trigonometricalfunctions of the displacement required, taking a given unit displacementto correspond to an angle of 211-. The alternating voltages are appliedto the stator windings of a resolver and the voltages induced in a rotorwinding of the resolver are used to operate a servo mechanism whichrotates the rotor until the induced voltage is zero. The rotor iscoupled mechanically to the device which is to be set to the givenposition.

The series of control knobs, operating in stepped fashion, is arrangedto provide alternating voltages related to the desired displacements indifferent orders, that is to say, a first control knob could becalibrated in multiples of 0.01 inch where 0.2 inch represents 21rwhereas a second control knob could be calibrated to provide incrementson that provided by the first control knob in multiples of 0.0001 inch.It is then required to produce according to the settings of the controlknobs voltages proportional to cos (A +3) and sin (A +B) for applicationto the stator windings of the resolver, where A and B are the anglescorresponding to the multiples of 0.01 inch and the multiples of 0.001inch respectively on the above angular scale. It may be shown that ifthese voltages are designated as V and V, respectively V a(cos AV tan B)and V x(sin AV tan B) A known position control system ultilising theserelations is illustrated schematically in FIGURE 1. An alternatingcurrent source 1 supplies current to an auto-transformer 2 which hastappings on it which provide voltages related to sine and cosinefractions of the voltage across the whole winding. Only a small numberof tappings is shown, although in practice a much larger number, say 25,would be used. These are selected according to the 3,4l9,774 PatentedDec. 31, 1968 position of the control knob used for Setting the value Awhich operates the ganged selector switches 3 and 4. Thus voltagesproportional to cos A and sin A are produced on the lines 5 and 6,respectively. The voltage V is produced on the line 7 by adding in thetransformer 9 a voltage proportional to V tan B, and the voltage V onthe line 8 by adding in the transformer 10 a voltage proportional to Vtan B. The voltage V, tan B is produced by feeding the voltage V fromthe line 8 to an autotransformer 11 which has tappings which, accordingto the position of a movable contact set by the control knob for settingthe value B, select a fraction tan B of the voltage applied to saidauto-transformer. The voltage V tan B is produced by feeding the voltageV from the line 7 to an auto-transformer 12 which similarly allows afraction tan B of the voltage V to be produced. The movable contacts onthe auto-transformers 11 and 12 are ganged so that a single control knobsets the position of both. The voltages V and V are applied to thequadrature stator windings 13 and 14 of the resolver 15. The rotor coil16 feeds its output to an amplifier 17 which in turn drives a motor 18ganged to the rotor until the voltage induced in the coil 16 is zero.

It will be observed that the system described in outline above requiresthree auto-transformer cores, namely those designated as 2, 11 and 12 inFIGURE 1. It is an object of the invention to provide an improvedposition control system wherein a lesser number of such cores isrequired thereby effecting economies in the construction of the system.

According to the invention there is provided a position control servomechanism including a resolver having first and second relativelymovable parts each provided with two inductors in quadrature, means forproducing and applying to the respective inductors on the first partalternating voltages respectively representing the sine and cosine of afirst angle, means for deriving an output voltage from one of theinductors on the second part, and means for producing relativedisplacement of the resolver parts in response to the output voltage ina sense tending to reduce the output voltage, wherein the improvementcomprises means for deriving a second output voltage from the other ofthe inductors on the second part, means for producing a fraction of thesecond output voltage, which fraction is dependent on a second angle,and means for adding the fraction of the second output voltage to theoutput voltage from the one of the inductors on the second part tomodify the latter output voltage, whereby the relative displacementtends to that represented by the sum of the first and second angles.

In one embodiment of the invention the means for producing and applyingalternating voltages includes means for generating a plurality ofalternating voltages respectively representing the sine and cosine of aseries of angles spaced apart by the same angular interval and means forselecting from among the voltages generated by the generating means, thevoltages respectively representing the sine and cosine of the firstangle, and the means for producing a fraction of the second outputvoltage includes auto-transformer means with a series of tappingsrespectively corresponding to a second series of angles smaller than theangular interval, and means for selecting from among the tappings, thetapping corresponding to the second angle.

In order that the invention may be clearly understood and readilycarried into effect, it will now be described with reference to theaccompanying drawings, in which:

FIGURE 1 illustrates schematically a known position control systemreferred to above, and

FIGURE 2 illustrates schematically and partially a position controlsystem according to the invention.

Referring to FIGURE 2, the voltages proportional to cos A and sin A arederived as already described with reference to FIGURE 1 on the lines 5and 6. These lines are similarly designated as 5 and 6 in FIGURE 2.These voltages are applied to the quadrature stator windings 19 and 20of a resolver which has quadrature rotor windings 21 and 22. If therotor is in such a position that the angle between the winding 21 and areference position parallel to the stator winding 19 is 0, then thevoltages induced in the windings 21 and 22 are proportional to cos (A0)and to sin (A-O) respectively. An error voltage, which is amplified bythe amplifier 17 which in turn drives the motor 18 ganged to the rotorand rotates it until the error voltage is zero, is derived by taking afraction tan B of the voltage proportional to cos (A0) and adding to itthe voltage proportional to sin (A-B). This is effected by applying thevoltage proportional to cos (A-O) across the winding 21 to anauto-transformer 23 provided with tappings which, according to theposition of a movable contact set by the control knob for setting thevalue B, select a fraction tan B of the voltage applied thereto.The'voltage derived thereby is added in the amplifier 17 to the voltageproportional to sin (A-B) from the winding 22. When the rotor hasreached its null position, that is to say the error voltage is zero,then sin (A6) +cos (A0) tan B=0 It may be shown that the expression onthe left hand side of this equation reduces to l/cos B. sin (A+B0) sothat the null condition reduces to sin (A-i-B0)=0 so long as cos B isnot zero. The latter condition will generally be fulfilled since B hasbeen regarded as an increment added to A and its value in the examplegiven would not exceed 0.01 of 2w. The condition sin (A+B-a)=0 issatisfied when 6--A +B, so that the rotor is set in the desiredposition. It will be observed that this system requires only two coresand is thus more economical than the known arrangement.

In some cases sufiicient accuracy may be obtained if a linear functionof B is used in place of a tangent function as described. In this casethe auto-transformer 23 with tappings arranged to follow a tangent lawis. replaced by one having evenly spaced taps. While the invention hasbeen described with reference to one embodiment it is not intended thatit should be limited thereto. In an alternative Way of carrying out theinvention, the conventional resolver elements may be replaced byInductosyn elements and of course butler amplifiers may be employedgenerally to avoid errors due to the loading of any output winding.

What I claim is:

1. A position control servo mechanism including a resolver having firstand second relatively movable parts each provided with twoinductors inquadrature, means for producing and applying to the respective inductorson the first part alternating voltages respectively representing thesine and cosine of a first angle, means for deriving an output voltagefrom one of the inductors on the second part, and means for producingrelative displacement of the resolver parts in response to the outputvoltage in a sense tending to reduce the output voltage, wherein theimprovement comprises means for deriving a second output voltage fromthe other of the inductors on the second part, means for producing afraction of the second output voltage, which fraction is dependent on asecond angle, and means for adding the fraction of the second outputvoltage to the output voltage from the one of the inductors on thesecond part to modify the latter output voltage, whereby the relativedisplacement tends to that represented by the sum of the first andsecond angles.

2. A servo mechanism according to claim 1, in which the means forproducing and applying alternating voltages includes means forgenerating a plurality of alternating voltages respectively representingthe sine and cosine of a series of angles spaced apart by the sameangular interval and means for selecting from among the voltagesgenerated by the generating means, the voltages respectivelyrepresenting the sine and cosine of the first angle, and the means forproducing a fraction of the second output voltage includesauto-transformer means with a series of tappings respectivelycorresponding to a second series of angles smaller than the angularinterval, and means for selecting from among the tappings, the tappingcorresponding to the second angle.

3. A servo mechanism according to claim 2, in which the means forproducing a fraction of the second output voltage is arranged toproportion the second output voltage as the tangent of the second angle.

4. A servo mechanism according to claim 1 in which the means forproducing a fraction of the second output voltage is arranged toproportion the second output voltage as the second angle.

References Cited UNITED STATES PATENTS 2,467,646 4/1949 Agins 318-28 X2,922,579 1/1960 Goldman 318-28 X 2,988,685 6/1961 Agins et a1 318-28 X3,042,307 7/1962 Booth et al. 235-186 3,296,427 1/1967 Clemence et a1.235-186 BENJAMIN DOBECK, Primary Examiner.

US. Cl. X.R. 235-186

1. A POSITION CONTROL SERVO MECHANISM INCLUDING A RESOLVER HAVING FIRSTAND SECOND RELATIVELY MOVABLE PARTS EACH PROVIDED WITH TWO INDUCTORS INQUADRATURE, MEANS FOR PRODUCING AND APPLYING TO THE REPECTIVE INDUCTORSON THE FIRST PART ALTERNATING VOLTAGES RESPECTIVELY REPRESENTING THESINE AND COSINE OF A FIRST ANGLE, MEANS FOR DERIVING AN OUTPUT VOLTAGEFROM ONE OF THE INDUCTORS ON THE SECOND PART, AND MEANS FOR PRODUCINGRELATIVE DISPLACEMENT OF THE RESOLVER PARTS IN RESPONSE TO THE OUTPUTVOLTAGE IN A SENSE TENDING TO REDUCE THE OUTPUT VOLTAGE, WHEREIN THEIMPROVEMENT COMPRISES MEANS FOR DERIVING A SECOND OUTPUT VOLTAGE FROMTHE OTHER OF THE INDUCTORS ON THE SECOND PART, MEANS FOR PRODUCING AFRACTION OF THE SECOND OUTPUT VOLTAGE, WHICH FRACTION IS DEPENDENT ON ASECOND ANGLE, AND MEANS FOR ADDING THE FRACTION OF THE SECOND OUTPUTVOLTAGE TO THE OUTPUT VOLTAGE FROM THE ONE OF THE INDUCTORS ON THESECOND PART TO MODIFY THE LATTER OUTPUT VOLTAGE. WHEREBY THE RELATIVEDISPLACEMENT TENDS TO THAT REPRESENTED BY THE SUM OF THE FIRST ANDSECOND ANGLES.